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@ -23,7 +23,7 @@ Her website is newly at **[https://dukenukemis.cool](https://dukenukemis.cool)**
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*Ashley is such a cutie.*
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**Why is she so based?** For example for the following reasons { Note that this is purely my interpretation of what I've seen/read on her website. ~drummyfish }: She is a pretty, biological woman (i.e. NOT some kind of angry [trans](tranny.md) [landwhale](fat.md)) BUT she shits on [feminism](feminism.md) and acknowledges plain facts about women such as that they usually need to be "put in line" (with [love](love.md)) by a man and that they are simply different. She makes a nice, ACTUALLY ENTERTAINING, well made politically incorrect stuff, her art is sincere, not trying to pretend anything or ride on some kind of fashion wave. { NOTE: Ashley pointed out that her site is NOT an art project or "social experiment". Indeed, this is not the intended meaning of the word "art" here, we simply mean "work" or "creation", just to make it clear. At LRS we kind of hate the word [work](work.md) so we often say "art" instead. ~drummyfish } She is VERY talented at comedy, hosts her OWN video website with a modest fan following and even though on [Jewtube](youtube.md) she could get hundred thousand times more followers and make a fortune, she doesn't do it because that would compromise her art and prevent her from doing what she really wants to do -- in fact recently she started to depart more into other topics, like technology repair, which probably in terms of popularity rather "hurts the numbers", but she just does it because it's what she likes and wants to do, it can be seen that she doesn't lust for simple popularity but rather for sharing truly interesting stuff. She does ask for donations but refuses to monetize her content with [ads](marketing.md) or [paywalls](paywall.md), creating a nice, pure, oldschool place on the Internet looks to truly be the one thing she's aiming for. She makes [fun](fun.md) of herself (like that she has a crush on [Duke Nukem](duke3d.md) lol), masterfully plays along with jokes blatantly sexualizing her and does some cool stuff like post measurements of her asshole and finding her porn lookalikes for the fanbase. It looks like she possesses some skills with technology (at least [Luke Smith](luke_smith.md) level), she supports [free software](free_software.md). She acknowledges the insanity of [pedophile](pedophilia.md) hysteria and proposes lowering age of consent (despite saying she was NOT a pedophile herself). She wants to normalize nudity, and doesn't shave her legs, she discourages makeup for females. Her website is quite nice, 1.0 style, with high [LRS](lrs_wiki.md)/[4chan](4chan.md)/[Dramatica](dramatica.md) vibes, there are "offensive" jokes but she stresses she in fact doesn't encourage violence, real racism and that she's not an extremist -- in one video she says she dislikes transsexuals and wants to make fun of gays but that in fact she doesn't mind any individual being gay or whatever, basically just opposing the political movements, propaganda, brainwashing etcetc., i.e. showing the exact same kind of attitude as us. She also understands Internet [culture](culture.md) and things like [trolling](trolling.md) being part of it -- in one video she clearly separates Internet and [real life](irl.md) and says you "can't apply real life logic on the Internet", that's very mature. By this she for example supports consensual incest. She even freaking has her own imageboard that's by the way very good (although now she says it's mostly occupied by retards, but she still keeps it running for them, that's very [selfless](selflessness.md)). She advocates [piracy](piracy.md) instead of giving money to [corporations](corporation.md): extremely based. She seems to see through propaganda and brainwashing, she says she does "not accept the reality" forced on her by this society, something we say and do as well, she shits on vaccines and likes cool "conspiracy theories". Yes, she seems SMART, she sees the power game of the elites, the propaganda, warns about it, shits on it. She seems to know how to write [English](english.md) without making 10 errors in every word. She advocates ETHICAL veganism, to spare animals of suffering. She hates [Elon Musk](elon_musk.md). She advocates not using cellphones and mainstream social networks. She does NOT have any [tattoos](tattoo.md). However, while all of these individual things are very nice, the **most important part**, and the one that basically matters above having certain opinion or demonstrating coolness in some way, is simply this: **she makes her own opinions**. As she states on the website, she doesn't accept any prefabricated "package of opinions", she thinks about things herself and makes HER OWN fucking decisions regardless of whether that leaves her alienated from the rest of human on the planet, and that's where all the coolness comes from -- this is the most important lesson Ashley can teach us.
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**Why is she so based?** For example for the following reasons { Note that this is purely my interpretation of what I've seen/read on her website. ~drummyfish }: She is a pretty, biological woman (i.e. NOT some kind of angry [trans](tranny.md) [landwhale](fat.md)) BUT she shits on [feminism](feminism.md) and acknowledges plain facts about women such as that they usually need to be "put in line" (with [love](love.md)) by a man and that they are simply different. She makes a nice, ACTUALLY ENTERTAINING, well made politically incorrect stuff, her art is sincere, not trying to pretend anything or ride on some kind of fashion wave. { NOTE: Ashley pointed out that her site is NOT an art project or "social experiment". Indeed, this is not the intended meaning of the word "art" here, we simply mean "work" or "creation", just to make it clear. At LRS we kind of hate the word [work](work.md) so we often say "art" instead. ~drummyfish } She is VERY talented at comedy, hosts her OWN video website with a modest fan following and even though on [Jewtube](youtube.md) she could get hundred thousand times more followers and make a fortune, she doesn't do it because that would compromise her art and prevent her from doing what she really wants to do -- in fact recently she started to depart more into other topics, like technology repair, which probably in terms of popularity rather "hurts the numbers", but she just does it because it's what she likes and wants to do, it can be seen that she doesn't lust for simple popularity but rather for sharing truly interesting stuff. She does ask for donations but refuses to monetize her content with [ads](marketing.md) or [paywalls](paywall.md), creating a nice, pure, oldschool place on the Internet looks to truly be the one thing she's aiming for. She makes [fun](fun.md) of herself (like that she has a crush on [Duke Nukem](duke3d.md) lol), masterfully plays along with jokes blatantly sexualizing her and does some cool stuff like post measurements of her asshole and finding her porn lookalikes for the fanbase. It looks like she possesses some skills with technology (at least [Luke Smith](luke_smith.md) level), she supports [free software](free_software.md). She acknowledges the insanity of [pedophile](pedophilia.md) hysteria and proposes lowering age of consent (despite saying she was NOT a pedophile herself). She wants to normalize nudity, and doesn't shave her legs, she discourages makeup for females. Her website is quite nice, 1.0 style, with high [LRS](lrs_wiki.md)/[4chan](4chan.md)/[Dramatica](dramatica.md) vibes, there are "offensive" jokes but she stresses she in fact doesn't encourage violence, real racism and that she's not an extremist -- in one video she says she dislikes transsexuals and wants to make fun of gays but that in fact she doesn't mind any individual being gay or whatever, basically just opposing the political movements, propaganda, brainwashing etcetc., i.e. showing the exact same kind of attitude as us. She also understands Internet [culture](culture.md) and things like [trolling](trolling.md) being part of it -- in one video she clearly separates Internet and [real life](irl.md) and says you "can't apply real life logic on the Internet", that's very mature. By this she for example supports consensual incest. She even freaking has her own imageboard that's by the way very good (although now she says it's mostly occupied by retards, but she still keeps it running for them, that's very [selfless](selflessness.md)). She advocates [piracy](piracy.md) instead of giving money to [corporations](corporation.md): extremely based. She seems to see through propaganda and brainwashing, she says she does "not accept the reality" forced on her by this society, something we say and do as well, she shits on vaccines and likes cool "conspiracy theories". Yes, she seems SMART, she sees the power game of the elites, the propaganda, warns about it, shits on it. She seems to know how to write [English](english.md) without making 10 errors in every word. She advocates ETHICAL veganism, to spare animals of suffering. She hates [Elon Musk](elon_musk.md). She advocates not using cellphones and mainstream social networks. She does NOT have any [tattoos](tattoo.md). However, while all of these individual things are very nice, the **most important part**, and the one that basically matters above having certain opinion or demonstrating coolness in some way, is simply this: **she makes her own opinions**. As she states on the website, she doesn't accept any prefabricated "package of opinions", she thinks about things herself and makes HER OWN fucking decisions regardless of whether that leaves her alienated from the rest of humans on the planet, and that's where all the coolness comes from -- this is the most important lesson Ashley can teach us.
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Sure, [we](lrs.md) find disagreements with her, for example on the question of [privacy](privacy.md), but if we call [Diogenes](diogenes.md) a based man and [Encyclopedia Dramatica](dramatica.md) a based website, we also have to admit Ashley Jones is a based woman and her website is likewise no less cool. At least at the time when this article was written. Even if she gets spoiled and one days turns 180 degrees from everything she stood for, the image of what she was will remain for others as an example, she is an original thinker and created something greater than a human can be: an immortal imagine of what one can hope to be.
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43
binary.md
43
binary.md
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@ -13,15 +13,17 @@ Of course the binary system didn't appear from nowhere, people in ancient times
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## Boolean Algebra ("True/False Logic")
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In binary we start by working with single [bits](bit.md) -- each bit can hold two values, 1 and 0. We may see bits now like "simple numbers", we'll want to do operations with them, but they can only ever be one of the two values. Though we can interpret these values in any way -- e.g. in electronics we see them as high vs low [voltage](voltage.md) -- in mathematics we traditionally turn to using [logic](logic.md) and interpret them as meaning *true* (1) and *false* (0). This will further allow us to apply all the knowledge and theory we have gathered about logic, such as formulas that allow us to simplify binary expressions etc.
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*For more detail see also [logic gate](logic_gate.md).*
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Next we want to define "operations" we can perform on single bits -- for this we use so called **[Boolean](bool.md) algebra**, which is originally a type of abstract algebra that works with [sets](set.md) and their operations such as conjunction, disjunction etc. Boolean algebra can be seen as a sort of simplified version of what we do in "normal" elementary school algebra -- just as we can add or multiply numbers, we can do similar things with individual bits, we just have a bit different operations such as logic [AND](and.md), logic [OR](or.md) and so on. Generally Boolean algebra can operate with more than just two values, however that's more interesting to mathematicians; for us all we need now is a binary Boolean algebra -- that's what programmers have adopted for their field. It is the case that in context of computers and programming we implicitly understand Boolean algebra to be the one working with 1s and 0s, i.e. the binary version, so the word **"boolean"** is essentially used synonymously with "binary" around computers. Many [programming languages](programming_language.md) have a [data type](data_type.md) called `boolean` or `bool` that allows represents just two values (*true* and *false*).
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In binary we start by working with single [bits](bit.md) -- each bit can hold two values, 1 and 0. At this point we may see bits like simple [numbers](number.md) and we'll want to start performing "operations" with them just like we are used to with ordinary numbers (What would numbers be good for if we could add them, subtract them etc.?), but it will still hold that bits can only ever hold one of the two values, 0 or 1, so it's naturally going to be a bit different. Though we can interpret what the 0 and 1 values mean in any way -- e.g. in electronics as high vs low [voltage](voltage.md) -- in mathematics we traditionally turn to go along with [logic](logic.md) and interpret them as *true* (1) and *false* (0). This interpretation is nice because math already has a lot of knowledge about laws of logic and this will transfer nicely to what we're doing now, so for example we'll be able to use various formulas that are already there and proven to work.
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The very basic operations, or logic [functions](function.md), of Boolean algebra are:
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Next we want to define these "operations" with bits -- for this we use so called **[Boolean](bool.md) algebra**, which is originally a type of abstract algebra that works with [sets](set.md) and operations such as conjunction, disjunction etc. Boolean algebra can be viewed as a sort of simplified version of what we do in "normal" elementary school algebra -- just as we can add or multiply numbers, we can do similar things with individual bits, we just have a bit different kinds of operations such as logical [AND](and.md) (similar to multiplication), logical [OR](or.md) (similar to addition) and so on. Generally Boolean algebra can operate with more than just two values (0 and 1), however that's more interesting to mathematicians; for us all we need now is a binary Boolean algebra -- that's what programmers have adopted. It is the case that in context of computers and programming we implicitly assume Boolean algebra to be the one working with 1s and 0s, i.e. the binary version, so the word **Boolean** is essentially used synonymously with "binary". Many [programming languages](programming_language.md) have a [data type](data_type.md) called `boolean` or `bool` that allows represents just two values (*true* and *false*).
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- **NOT** (negation, `!`): Done with single bit, turns 1 into 0 and vice versa.
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- **[AND](and.md)** (conjunction, `/\`): Done with two bits, yields 1 only if both input bits are 1, otherwise yields 0. This is similar to multiplication (1 * 1 = 1, 1 * 0 = 0, 0 * 1 = 0, 0 * 0 = 0) .
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- **[OR](or.md)** (disjunction, `\/`): Done with two bits, yields 1 if at least one of the input bits is 1, otherwise yields 0. This is similar to addition (1 + 1 = 1, 1 + 0 = 1, 0 + 1 = 1, 0 + 0 = 0).
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The very basic operations, or now we would rather say Boolean [functions](function.md), are:
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- **NOT** (negation, `!`): Performed on a single bit, turns 1 into 0 and vice versa.
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- **[AND](and.md)** (conjunction, `/\`): Performed on two bits, yields 1 only if both input bits are 1, otherwise yields 0. This is similar to multiplication (1 * 1 = 1, 1 * 0 = 0, 0 * 1 = 0, 0 * 0 = 0) .
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- **[OR](or.md)** (disjunction, `\/`): Performed on two bits, yields 1 if at least one of the input bits is 1, otherwise yields 0. This is similar to addition (1 + 1 = 1, 1 + 0 = 1, 0 + 1 = 1, 0 + 0 = 0).
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There are also other function such as [XOR](xor.md) (exclusive OR, is 1 exactly when the inputs differ) and negated versions of AND and OR (NAND and NOR, give opposite outputs of the respective non-negated function). The functions are summed up in the following table (we all these kinds of tables **truth tables**):
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| 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
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| 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
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In fact there exists more functions with two inputs and one output (16 in total, computing this is left as exercise :]). However not all are named -- we only use special names for the commonly used ones, mostly the ones in the table above.
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In fact there exists more functions with two inputs and one output (16 in total, computing this is left as an exercise :]). However not all have commonly established names -- we only use special names for the commonly used ones, mostly the ones in the table above.
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An interesting thing is that we may only need one or two of these functions to be able to create all other function (this is called *functional completeness*); for example it is enough to only have *AND* and *NOT* functions together to be able to construct all other functions. Functions *NAND* and *NOR* are each enough by themselves to make all the other functions! For example *NOT x = x NAND x*, *x AND y = NOT (x NAND y) = (x NAND y) NAND (x NAND y)*, *x OR y = (x NAND x) NAND (y NAND y)* etc.
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@ -58,28 +60,28 @@ Boolean algebra further tells us some basic laws we can use to simplify our expr
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- NOT (x OR y) = NOT(x) AND NOT(y)
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- ...
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By combining all of these simple functions it is possible to construct not only operations with whole numbers and traditional algebra, but also a whole computer that renders 3D graphics and sends multimedia over the Internet. For more details see **[logic circuits](logic_circuit.md)**.
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By combining all of these simple functions it is possible to go on and construct not only operations with whole numbers and the traditional algebra we know from school, but also a whole computer that renders 3D graphics and sends multimedia over the Internet. This is done by grouping multiple bits together to create a base-2 numeral system (described below), i.e. we'll go from working with single bits to working with GROUPS of bits -- single bits only allow us to represent two values, but a group of bits will allow us to store more. For example a group of 8 bits ([byte](byte.md)) lets us represent 256 distinct values, which we may interpret as whole numbers: 0 to 255. Now using the elementary functions shown above we can implement all the traditional operators for addition, subtraction, multiplication, division, ... and that's not all; we can go yet further and implement negative numbers, fractions, later on strings of text, and we can go on and on until we have a very powerful system for computation. For more detail see [logic gates](logic_gate.md) and [logic circuits](logic_circuit.md).
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## Base-2 Numeral System
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While we may use a single bit to represent two values, we can group more bits together and become able to represent more values; the more bits we group together, the more values we'll be able to represent as possible combinations of the values of individual bits. The number of bits, or "places" we have for writing a binary number is called a number of bits or **bit width**. A bit width *N* allows for storing 2^*N* values -- e.g. with 2 bits we can store 2^2 = 4 values: 0, 1, 2 and 3, in binary 00, 01, 10 and 11. With 3 bits we can store 2^3 = 8 values: 0 to 7, in binary 000, 001, 010, 011, 100, 101, 110, 111. And so on.
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While we may use a single bit to represent two values, we can group more bits together and so gain the ability to represent more values; the more bits we group together, the more values we'll be able to represent as possible combinations of the values of individual bits. The number of bits, or "places" we have for writing a binary number is called a number of bits or **bit width**. A bit width *N* allows for storing 2^*N* values -- e.g. with 2 bits we can store 2^2 = 4 values: 0, 1, 2 and 3, in binary 00, 01, 10 and 11. With 3 bits we can store 2^3 = 8 values: 0 to 7, in binary 000, 001, 010, 011, 100, 101, 110, 111. And so on.
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At the basic level binary works just like the [decimal](decimal.md) (base 10) system we're used to. While the decimal system uses powers of 10, binary uses powers of 2. Here is a table showing a few numbers in decimal and binary:
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At the basic level binary works just like the [decimal](decimal.md) (base 10) system we're used to. While the decimal system uses powers of 10, binary uses powers of 2. Here is a table showing a few numbers in decimal and binary (with 4 bits):
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| decimal | binary |
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| ------- | ------ |
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| 0 | 0 |
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| 1 | 1 |
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| 2 | 10 |
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| 3 | 11 |
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| 4 | 100 |
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| 5 | 101 |
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| 6 | 110 |
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| 7 | 111 |
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| 0 | 0000 |
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| 1 | 0001 |
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| 2 | 0010 |
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| 3 | 0011 |
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| 4 | 0100 |
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| 5 | 0101 |
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| 6 | 0110 |
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| 7 | 0111 |
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| 8 | 1000 |
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| ... | ... |
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**Conversion to decimal**: let's see an example that utilizes the facts mentioned above. Let's have a number that's written as 10135 in decimal. The first digit from the right (5) says the number of 10^(0)s (1s) in the number, the second digit (3) says the number of 10^(1)s (10s), the third digit (1) says the number of 10^(2)s (100s) etc. Similarly if we now have a number **100101** in binary, the first digit from the right (1) says the number of 2^(0)s (1s), the second digit (0) says the number of 2^(1)s (2s), the third digit (1) says the number of 2^(2)s (4s) etc. Therefore this binary number can be converted to decimal by simply computing 1 * 2^0 + 0 * 2^1 + 1 * 2^2 + 0 * 2^3 + 0 * 2^4 + 1 * 2^5 = 1 + 4 + 32 = **37**.
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**Conversion to decimal**: let's see an example demonstrating things mentioned above. Let's have a number that's written as 10135 in decimal. The first digit from the right (5) says the number of 10^(0)s (1s) in the number, the second digit (3) says the number of 10^(1)s (10s), the third digit (1) says the number of 10^(2)s (100s) etc. Similarly if we now have a number **100101** in binary, the first digit from the right (1) says the number of 2^(0)s (1s), the second digit (0) says the number of 2^(1)s (2s), the third digit (1) says the number of 2^(2)s (4s) etc. Therefore this binary number can be converted to decimal by simply computing 1 * 2^0 + 0 * 2^1 + 1 * 2^2 + 0 * 2^3 + 0 * 2^4 + 1 * 2^5 = 1 + 4 + 32 = **37**.
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```
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100101 = 1 + 4 + 32 = 37
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10010
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```
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All of these operations can be implemented just using the basic boolean functions -- see [logic circuits](logic_circuit.md) and [CPUs](cpu.md).
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All of these operations can be implemented just using the basic boolean functions described in the section above -- see [logic circuits](logic_circuit.md) and [CPUs](cpu.md).
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In binary it is very simple and fast to divide and multiply by powers of 2 (1, 2, 4, 8, 16, ...), just as it is simply to divide and multiple by powers of 10 (1, 10, 100, 1000, ...) in decimal (we just shift the radix point, e.g. the binary number 1011 multiplied by 4 is 101100, we just added two zeros at the end). This is why as a programmer **you should prefer working with powers of two** (your programs can be faster if the computer can perform basic operations faster).
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- [nullary](nullary.md)
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- [unary](unary.md)
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- [ternary](ternary.md)
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- [logic gate](logic_gate.md)
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- [logic circuit](logic_circuit.md)
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- [bit](bit.md)
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- [hexadecimal](hexadeciaml.md)
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187
calculus.md
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187
calculus.md
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# Calculus
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100% UNDER CONSTRUCTION
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{ BEWARE: I am not a mathematician, this will be dumbed down for noobs and [programmers](programming.md) like me, actual mathematicians may suffer brain damage reading this. ~drummyfish }
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Calculus is a bit infamous but hugely important area of advanced [mathematics](math.md) whose focus lies in studying **continuous change**: for example how quickly a [function](function.md) grows, how fast its growth "accelerates", in which direction a multidimensional function grows the fastest etc. This means in calculus we stop being preoccupied with actual immediate values and start focusing on their CHANGE: things like velocity, acceleration, slopes, gradients etc., in a highly generalized way. Calculus is one of the first disciplines one gets confronted with in higher math, i.e. when starting University, and for some reason it's a very feared subject among students to whom the name sounds like a curse, although the basics aren't more difficult than other areas of math (that's not to say it shouldn't be feared, just that other areas should be feared equally so). Although from high school textbooks it's easy to acquire the impression that all problems can be solved without calculus and that it will therefore be of little practical use, the opposite is in fact true: in [real world](irl.md) EVERYTHING is about change, proof of which is the fact that in [physics](physics.md) most important phenomena are described by **[differential equations](differential_equation.md)**, i.e. basically "calculus equations" -- it turns out that many things depend on rate of change of some variable rather than the variable's direct value: for example air friction depends on how fast we are moving (how quickly our position is changing), our ears hear thanks to CHANGE in air pressure, electric current gets generated by CHANGE of magnetic field etc. Calculus is very similar to (and sometimes is interchangeably used with) *mathematical analysis* (the difference is basically that analysis tries to [prove](prove.md) what calculus does, at least according to the "[Internet](internet.md)"). The word *calculus* is also sometimes used to signify any "system for making calculations", for example [lambda calculus](lambda_calculus.md).
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Is this of any importance to a programmer? Fucking YES, you can't avoid it. Consider [physics engines](physics_engine.md), [machine learning](machine_learning.md), smooth [curves](curve.md) and surfaces in computer graphics, [interpolation](interpolation.md) and animation, scientific simulations, [electronics](electronics.md), [robotics](robotics.md), [signal](signal.md) processing and other kind of various shit all REQUIRE at least basics of calculus.
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In essence there are two main parts to calculus, two mathematical "operations" that work with functions and are opposite to each other:
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- **Derivative** (differentiation): says how (how fast and in which direction) a given function changes.
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- **Integral** (integration): opposite of derivative -- given a function of "change" we get back the original function (well, this is just one possible way to view it, but sufficient for now).
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One thing shows here: one of the reasons why calculus is considered advanced is probably that instead of simple numbers we suddenly start working with whole [functions](function.md), i.e. we have operators that we apply to function and we get new functions -- this requires some more [abstract](abstraction.md) thinking as a function is harder to image than a number. But then again it's not anything too difficult, it just requires some preliminary study to get familiar with what a function actually is etc.
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Now listen up, here comes the truth about calculus. Doing it correctly and precisely is difficult and sometimes literally impossible, and this is left for mathematicians. Programmers and engineers HAVE TO know the basic theory, but we are largely saved by one excellent thing: **[numerical](numerical.md) methods**. We can compute derivatives and integrals only [approximately](approximation.md) with algorithms that always work for any function and which will be [good enough](good_enough.md) for almost everything we ever encounter in practice. Besides in [digital](digital.md) computers we deal almost exclusively with non-continuous functions anyway, we just have very dense discrete sets of points because in the end we only have finite memory, integer values and sampled data, so there is nothing more natural than numerical methods here. So where a mathematician spends years trying to figure out how to precisely sum up infinitely many infinitely small parts of some weird function, we just write a program that sums up a very big number of very tiny parts and call it a day. Still there exist programs for so called *symbolic computation* that try to automatically do what the mathematician does, i.e. apply reasoning to get precise results, but these belong to some quite specialized areas.
|
||||
|
||||
TODO: graph
|
||||
|
||||
## Derivative
|
||||
|
||||
Derivative finds how **quickly a function grows** at any given point. DOING derivatives is called **differentiation** (confusingly because differential is a term distinct from derivative). Since derivative and integral are opposite operations, one would assume they'd be equally difficult to handle, but no, derivative is the **easier** part! So it's always taught first. It's kind of like multiplication and division -- multiplication is a bit easier (division has remainders, undefined division by zero etc.).
|
||||
|
||||
NOTE on notation: there are several notations used for derivatives. We will use a very simple one here: *f'(x)* to us is the derivative of a function *f(x)*. Mathematicians will probably rather like to write *d/dx f(x)*. Just know that this is a thing.
|
||||
|
||||
OK, BUT **what exactly IS this "derivative"? What does it say?** Basically derivative is the **tangent** to the graph of a function at given point. Derivative of function *f(x)* is a new function *f'(x)* which for given *x* says the **slope** of the graph of function *f(x)* at the point *x*. Slope here means literally the [tangent](tan.md) function which encodes the angle at which the function is increasing (or decreasing). Tangent is defined as the (unitless) ratio of vertical change to horizontal change (for example if a plane is ascending with tangent equal to 2, we know that for every horizontal meter it gains two meters of height). Note that this is mathematically idealized so that no matter how quickly the function changes we really mean the slope at the exact single point, i.e. imagine drawing a tangent line to the graph of the function and then measuring how quickly it changes vertically versus how quickly it changes horizontally. Mathematicians define this using [limits](limit.md) and infinitesimal intervals, but we don't have to care too much about that now, let's just assume it [magically](magic.md) all works now.
|
||||
|
||||
Here it is show graphically:
|
||||
|
||||
```
|
||||
tangent / __
|
||||
line / .' ''..
|
||||
/ __.'f(x)
|
||||
/-''
|
||||
/|
|
||||
__../:|dy
|
||||
_-' /__|
|
||||
/ dx
|
||||
/ :
|
||||
/ :
|
||||
:
|
||||
--------+--------------->x
|
||||
A
|
||||
```
|
||||
|
||||
Here we see a tangent line drawn at the graph of function *f(x)* at point *A*. We can draw the small right triangle and like shown -- the derivative at point *A* is now literally computed by dividing *dy* by *dx*. We can actually try to approximate the ideal derivative (and this is kind of how computers do it with the numerical methods) by computing
|
||||
*(f(x + C) - f(x)) / C* where *C* we set to some small number, for example 10^-10. It's basically how it's mathematically defined too, mathematicians just set the *C* to "infinitely small distance". By this notice the that the derivative will be:
|
||||
|
||||
- 0 if the function is monotonic (i.e. going "horizontally", neither increasing nor decreasing). This is because *dy* will be 0 and 0 divided by any *dx* will be 0. This fact is used especially when we're finding where functions have minimum and maximum values as we know at these extreme values they will be monotonic.
|
||||
- > 0 if the function is increasing. This is because *dy* will be positive and since *dx* is always positive, we'll get a positive number by dividing them.
|
||||
- < 0 if the function is decreasing. This is because *dy* will be negative and negative divided by positive *dx* is negative.
|
||||
|
||||
Now it's important to say that derivatives can only be done with **differentiable** functions, i.e. ones that in fact DO have a derivative. This cyclic definition only says there indeed exist functions which are NOT differentiable -- imagine for example a function *f(x)* that gives 0 for every *x* except when *x = 1* where *f(1) = 1* -- what's slope of such function at *x = 1*? How the hell do you wanna integrate that? Firstly it's infinite (the tangent line goes completely vertically and here computing *dy/dx* just results in division by zero), but we don't even know if it's going up or down (it goes up from left but down to the right), it's just fucked up. Also a function that has holes (is not defined everywhere) clearly also isn't differentiable because if there's nothing to differentiate then what do you wanna do? A function that's not differentiable everywhere may still be differentiable in certain parts of course, but in general if we claim a function is differentiable we imply it's differentiable everywhere. It may also be the case that a function is differentiable but its derivative is not. Actually it further gets a bit more complicated, functions may also be partially differentiable, it is possible that a derivative may exist only from "one side", but we won't go into this. There exist conditions that must hold in order for a function to be differentiable, for example it must be continuous and smooth and whatever, just look that up if you need.
|
||||
|
||||
OK so to actually compute a derivative of a function we can use some of the following rules:
|
||||
|
||||
| *f(x)* | *f'(x)* |
|
||||
| ---------------------- | ----------------------------- |
|
||||
| *n* | *0* |
|
||||
| *x^n* | *n * x^(n-1)* |
|
||||
| *e^x* | *e^x* |
|
||||
| *sin(x)* | *cos(x)* |
|
||||
| *cos(x)* | *-sin(x)* |
|
||||
| *ln(x)* | *1/x* |
|
||||
| *a * g(x)* | *a * g'(x)* |
|
||||
| *g(x) + h(x)* | *g'(x) + h'(x)* |
|
||||
| *g(x) * h(x)* | *g'(x) * h(x) + g(x) * h'(x)* |
|
||||
| *g(h(x))* | *g'(h(x)) * h'(x)* |
|
||||
|
||||
**Monkey example**: let's try to find the derivative of this super retarded function:
|
||||
|
||||
*f(x) = x^2 - 2 * x + 3*
|
||||
|
||||
Its graph looks like this:
|
||||
|
||||
```
|
||||
:| :
|
||||
3 + :
|
||||
|: :
|
||||
2 + '.._..'
|
||||
|
|
||||
1 +
|
||||
|
|
||||
--+----+----+----+--
|
||||
-1 0| 1 2
|
||||
|
|
||||
```
|
||||
|
||||
To differentiate this function we only need to know (from the table above) that a derivative of a sum equals sum of derivatives and then just invoke a simple rule: derivative of *x^N* is *N * x^(N-1)*. We have very little [work](work.md) to do here because there are no composed functions and similar shit, so we simply get:
|
||||
|
||||
*f'(x) = 2 * x - 2*
|
||||
|
||||
So *x^2* became *2 * x*, *-2 * x* became just -2 (because *x^0 = 1*) and *3* just disappeared (this always happens to additive constants -- notice that such constants don't affect the function's slope in any way, so that's why). The graph of the derivative looks like this:
|
||||
|
||||
```
|
||||
|
|
||||
2 + /
|
||||
| /
|
||||
1 + /
|
||||
| /
|
||||
--+----+----+----+--
|
||||
-1 0| /1 2
|
||||
| /
|
||||
-1+ /
|
||||
|/
|
||||
-2+
|
||||
```
|
||||
|
||||
Things to notice here are:
|
||||
|
||||
- The derivative has value 0 at *x = 1*, which means the function is monotonic at this point -- checking out the graph of the original function we see it really is so, the function turns there from decreasing to increasing.
|
||||
- Before *x = 1* the derivative is negative, meaning the function is decreasing (checks out). The slope is also increasing gradually, meaning the function slows down in decreasing its value.
|
||||
- After *x = 1* the opposite is true: the slope is positive and starts increasing, i.e. the function starts increasing AND it keeps increasing faster and faster.
|
||||
- ...
|
||||
|
||||
**OK but what if we differentiate the derivative lol?** This is legit, it will give us a **higher order derivative** and it is very useful and common. When we see the first derivative as the "speed" of the function's change, the second order derivative gives us the "speed" of the speed of function's change, i.e. basically it's acceleration. We will write second order derivative of function *f(x)* as *f''(x)*. This can for example tell us where the function is convex versus concave (how it is "bent"), which again helps with finding minimum and maximum values etc. Of course we may continue and make third order derivative, fourth etc.
|
||||
|
||||
Next we must mention **partial derivatives** which are basically **multidimensional** derivatives, i.e. ones we do with functions of multiple variables. There is one important thing to mention: when differentiating a function of multiple variables, we have to say which variable we are differentiating against, which is an equivalent of choosing the axis along which we differentiate. Practically this will result in us treating the non-chosen variables as if they were constants. So say we have a function of two variables *f(x,y)*: we can differentiate it against the variable *x* and also *y*, i.e. we get two different derivatives. If we imagine the function *f(x,y)* as a two dimensional [heightmap](heightmap.md), then the derivative against *x* means we are getting a slope as if we're going in the *x* axis direction (and accordingly the same holds for *y*). This is why it's called *partial* derivatives: there are multiple derivatives, multiple *parts*. Making a [vector](vector.md) out of all partial derivatives will give us a **[gradient](gradient.md)** which is kind of an "arrow" that can tell us in which direction the increase/decrease if the fastest. This is very important for example for machine learning where we are trying to minimize the error function by following the path of the gradient etc. All this is beyond the scope of this article though.
|
||||
|
||||
## Integral
|
||||
|
||||
Integral is the opposite to derivative. There are usually two main ways to interpret what an integral means:
|
||||
|
||||
- Literally the opposite of derivative, i.e. it takes a function, which is interpreted as the rate of change, and gives us back the original function.
|
||||
- Geometric interpretation: integral gives the [area](area.md) under the graph of a function, while taking the area below zero to be negative. This is subsequently seen as a **[sum](sum.md)** of infinitely many small "strips" into which we cut the graph of the function. All in all integral can be though of as a kind of fancy sum, and even they symbol for it is a big weird *S*.
|
||||
|
||||
Both of these interpretations are equivalent in that we will compute the same thing, they only differ in how we think of what we are computing.
|
||||
|
||||
As already claimed in the section on derivative, integrating is **more difficult** than differentiation. Some reasons for this are:
|
||||
|
||||
- There is no simple [algorithm](algorithm.md) for integrating general function (only for some specific cases) and many functions do NOT have analytical solutions at all! I.e. while we can make a derivative of any (differentiable) function by just following simple rules, getting an integral of a function is often a matter of trial and error, integrating is kind of [art](art.md) that has to be learned. This may come as a surprise but it is so, it is similar to how for example factoring a number is much more difficult than multiplying the factors back.
|
||||
- Unlike with derivatives there are infinitely many integrals of given function because functions that only differ by an added constant will give the same derivative (for example the functions *f(x) = x* and *f(x) = x + 1* will both have the same derivative) -- so when we're integrating we always get function that has a variable additive constant in it.
|
||||
- Integrals don't have some nice mathematical properties that derivatives have, so we can't assume as much, for example a derivative of an elementary function is always elementary function but this is not the case for an integral. { At least I think :) ~drummyfish }
|
||||
- Integrating a function makes it more complex (e.g. the exponents of variables increase), unlike with derivatives where we are simplifying the function.
|
||||
- Integrals don't usually make sense at single points, they are related to [intervals](interval.md). While with derivatives it's completely fine to ask "what's the derivative of this function at this single point", with integrals we always have to as "what's the integral between points A and B".
|
||||
- As a consequence of the previous point there are TWO types of integrals: definite and indefinite.
|
||||
|
||||
So due to these complications we now yet have to explain the two different types of integrals:
|
||||
|
||||
- **indefinite integral**: This is the FUNCTION we get by performing integration, i.e. result of indefinite integral is a mathematical expression with variables in it. In fact this expression represents an infinite set of functions because it always has the additive constant *C* in it (like hinted above) -- we can kind of ignore this for now. The important gist is this: indefinite integral kind of gives us a general FORMULA that can further be used to compute definite integrals. For example an indefinite integral of function *f(x) = 1* will be *x + C*. In practice the result we are searching is often a definite integral (a single value), but to compute that we have to start by computing the indefinite integral.
|
||||
- **definite integral**: This is a single [NUMBER](number.md) which (applying the geometric interpretation of integral) tells us the AREA below the function graph (with area below zero counting as negative) over some specific INTERVAL, i.e. between two given points A and B. This means that definite integral doesn't give us an expression but rather a quantity. For example a definite integral of function *f(x) = 1* over interval [0,1] will give us 1 (imagine the graph: the area is simply that of a square with side 1). Definite integrals are computed from the indefinite integral by plugging the upper interval number into the indefinite integral (in the place of the variable), then plugging the lower interval number, and then subtracting the latter from the former. With numeric methods (computer integration) we always only get definite integrals (and actually only their approximate values) -- the computer here skips computing the indefinite integral (as that's hard) and rather like a dumb machine LITERALLY goes by small steps and computes the area below the function graph.
|
||||
|
||||
**Example**: we will now try to make an indefinite integral of the function:
|
||||
|
||||
*f(x) = 2 * x - 2*
|
||||
|
||||
This is the derivative we got in the example of differentiation, so by integrating we should get back the original function we differentiated there.
|
||||
|
||||
Now for the **notation**: the symbol for integral is kind of a big italic *S* ([Unicode](unicode.md) U+222), but for [simplicity](kiss.md) we will just use the uppercase letter *I* here. With indefinite integrals only the symbol alone is used. For definite integrals we additionally write the interval over which we make the integral, i.e. *I(A,B)* (normally *A* is written at the bottom and *B* at the top), where *A* and *B* says the interval. So we will now write our indefinite integral like this:
|
||||
|
||||
*I 2 * x - 2 dx*
|
||||
|
||||
**Wait dude WHAT THE FUCK is this dx shit at the end?** This question is expected. Look: it has to do with the theory behind what the integral mathematically means, for starters one can just ignore it and remember that integral starts with *I*, then the integrated function follows, and then there is *dx* at the end. But to give a bit of explanation: firstly notice the *dx* tells us what the integrated variable is -- usually we have a function with single variable *x* and so it's pretty clear, but once we move to more dimensions we'll have more variables and this *dx* tells us what is a variable (i.e. along which axis we are integrating) and what is to be treated as a constant (maybe this doesn't yet make much sense but with integration there is a big difference between a variable and a constant, even if they are both represented by a letter). The real reason for *dx* is that the integral really represents an **infinite sum**. Have you ever seen that big sigma symbol for a sum? The integral symbol (here *I*) is like this, it likewise says "make an infinite sum of what will follow". But if we take a function and make infinitely many steps and keep summing the values the function gives us, we will just get [infinity](infinity.md) as the sum, so something is missing. In fact we don't want to sum the function values but rather areas of "tiny strips" we are kind of drawing below the function graph -- now a strip is basically a rectangle: area of a rectangle is computed as its height times its width. Height of the rectangle is the function value (here *2 * x - 2*) and width is *dx*, which represents the "infinitely narrow" interval. This is just to give some idea about WHY it looks like this, but it's cool to ignore it for now.
|
||||
|
||||
So now the fuck we can finally move on. Our integral is really easy because it's just a sum of two expressions (and an integral of a sum thankfully equals a sum of integrals) that can be integrated easily. So from the rule *I N * x dx = x^(N + 1) / N* we deduce that integral of *2 * x* is *2 * x^3 / 2 = x^3* and integral of *-2* is *-2 * x*, so we get:
|
||||
|
||||
*I 2 * x - 2 dx = x^3 - 2 * x + C*
|
||||
|
||||
A few things to note here now:
|
||||
|
||||
- Notice the additive constant *C* at the end. We always have to include this constant in the result of indefinite integral, like already mentioned. For example imagine if we set *C = 0*, then we'll get a function *x^3 - 2 * x*, and if we differentiate this back, we'll get the function we integrated: *2 * x - 2*. But we will also get the same function no matter what *C* we set because, like explained in the derivative section, additive constants disappear in differentiation. So just never forget this constant. We didn't obtain a single function but an infinite set of functions that differ just by the value of *C* (i.e. their graphs are just vertically shifted).
|
||||
- We in fact DID receive back the original function from the derivative example, which was *x^3 - 2 * x + 3*, which confirms our result as correct. Or, as per above, we should rather say again that this function is a part of the set of functions we computed, one with *C = 3*.
|
||||
|
||||
Our example integral wasn't that hard, right? Yes, this was extremely easy, but once you start integrating something with composed functions (functions inside other functions) you'll get into all sorts of trouble.
|
||||
|
||||
Now let's finish with computing a definite integral, OK? Let's say we want to compute the integral over interval 0 to 1, i.e. we'll write:
|
||||
|
||||
*I(0,1) 2 * x - 2 dx*
|
||||
|
||||
Above we said this is done by computing indefinite integral (already done), then plugging the upper and lower bound and subtracting, so let's do it:
|
||||
|
||||
*I(0,1) 2 * x - 2 dx = (1^3 - 2 * 1 + C) - (0^3 - 2 * 0 + C) = -1*
|
||||
|
||||
Things to notice here:
|
||||
|
||||
- The constants *C* nicely subtract and disappear, and they always will, so we don't have to worry about assigning them any values or stuff like that.
|
||||
- The area we got is negative and its absolute size is 1, does this make sense? YES. Take a look at the graph of the function *2 * x - 2* up above and pay attention to the interval 0 to 1. The function's value is below zero and we said that area below zero will be negative, so this checks out. Also we can see that geometrically the size of the area is a half of a rectangle of height 2 and width 1, which is exactly 1. So all in all we're cool.
|
||||
|
||||
TODO: the rules
|
||||
|
||||
**Can we do higher order integrals and partial integrals?** Yes, of course, just like with derivatives we can do both of these.
|
||||
|
||||
## See Also
|
||||
|
||||
- [differential equation](differential_equation.md)
|
||||
3
derivative.md
Normal file
3
derivative.md
Normal file
|
|
@ -0,0 +1,3 @@
|
|||
# Derivative
|
||||
|
||||
See [calculus](calculus.md).
|
||||
3
integral.md
Normal file
3
integral.md
Normal file
|
|
@ -0,0 +1,3 @@
|
|||
# Integral
|
||||
|
||||
See [calculus](calculus.md).
|
||||
|
|
@ -28,6 +28,7 @@ There exist many terms that are highly similar and can legitimately be used inte
|
|||
- **[brute force](brute_force.md)** vs **[heuristic search](heuristic_search.md)**
|
||||
- **[buffer](buffer.md)** vs **[cache](cache.md)** vs **[cash](money.md)**
|
||||
- **[bug](bug.md)** vs **[glitch](glitch.md)** vs **[error](error.md)** vs **[exception](exception.md)** vs **[fault](fault.md)** vs **[failure](fail.md)** vs **[defect](defect.md)**
|
||||
- **[calculus](calculus.md)** vs **mathematical analysis**
|
||||
- **[causation](causation.md)** vs **[correlation](correlation.md)** (le [reddit](reddit.md) scientist rule)
|
||||
- **[cepstrum](cepstrum.md)** vs **[spectrum](spectrum.md)**
|
||||
- **[chaos](chaos.md)** vs **[randomness](random.md)** vs **[pseudorandomness](pseudorandom.md)** vs **[quasirandomness](quasirandomness.md)** vs **[entropy](entropy.md)** vs **[statistics](statistics.md)** vs **[probability](probability.md)** vs **[stochasticity](stochastic.md)**
|
||||
|
|
@ -63,6 +64,7 @@ There exist many terms that are highly similar and can legitimately be used inte
|
|||
- **[democracy](democracy.md)** vs **[voting](voting.md)**
|
||||
- **demonstration** vs **[proof](proof.md)**
|
||||
- **[desktop environment](de.md)** vs **[window manager](wm.md)** vs **[windowing system](windowing_system.md)**
|
||||
- **[derivative](derivative.md)** vs **[differential](differential.md)**
|
||||
- **[discretization](discretization.md)** vs **[quantization](quantization.md)**
|
||||
- **[duck typing](duck_typing.md)** vs **[weak typing](weak_typing.md)** vs **[dynamic typing](dynamic_typing.md)** vs **[no typing](untyped.md)**
|
||||
- **[digit](digit.md)** vs **[number](number.md)** vs **[value](value.md)** vs **figure** vs **numeral**
|
||||
|
|
|
|||
3616
random_page.md
3616
random_page.md
File diff suppressed because it is too large
Load diff
File diff suppressed because one or more lines are too long
119
wiki_stats.md
119
wiki_stats.md
|
|
@ -3,9 +3,9 @@
|
|||
This is an autogenerated article holding stats about this wiki.
|
||||
|
||||
- number of articles: 612
|
||||
- number of commits: 943
|
||||
- total size of all texts in bytes: 4803185
|
||||
- total number of lines of article texts: 35358
|
||||
- number of commits: 944
|
||||
- total size of all texts in bytes: 4811795
|
||||
- total number of lines of article texts: 35380
|
||||
- number of script lines: 294
|
||||
- occurrences of the word "person": 9
|
||||
- occurrences of the word "nigger": 103
|
||||
|
|
@ -35,60 +35,80 @@ longest articles:
|
|||
|
||||
top 50 5+ letter words:
|
||||
|
||||
- which (2642)
|
||||
- there (2080)
|
||||
- people (1973)
|
||||
- example (1629)
|
||||
- other (1509)
|
||||
- about (1324)
|
||||
- which (2647)
|
||||
- there (2083)
|
||||
- people (1976)
|
||||
- example (1634)
|
||||
- other (1510)
|
||||
- about (1325)
|
||||
- number (1288)
|
||||
- software (1228)
|
||||
- because (1048)
|
||||
- their (1026)
|
||||
- software (1234)
|
||||
- because (1051)
|
||||
- their (1030)
|
||||
- program (1020)
|
||||
- would (996)
|
||||
- something (956)
|
||||
- being (951)
|
||||
- would (997)
|
||||
- something (959)
|
||||
- being (952)
|
||||
- things (920)
|
||||
- language (915)
|
||||
- called (890)
|
||||
- simple (821)
|
||||
- computer (817)
|
||||
- computer (818)
|
||||
- numbers (813)
|
||||
- without (806)
|
||||
- without (807)
|
||||
- however (758)
|
||||
- different (756)
|
||||
- different (758)
|
||||
- programming (751)
|
||||
- these (742)
|
||||
- function (741)
|
||||
- world (723)
|
||||
- world (722)
|
||||
- system (696)
|
||||
- doesn (677)
|
||||
- should (673)
|
||||
- still (664)
|
||||
- games (656)
|
||||
- while (648)
|
||||
- doesn (679)
|
||||
- should (675)
|
||||
- still (666)
|
||||
- games (657)
|
||||
- while (649)
|
||||
- drummyfish (633)
|
||||
- point (632)
|
||||
- drummyfish (631)
|
||||
- society (630)
|
||||
- society (631)
|
||||
- simply (620)
|
||||
- possible (608)
|
||||
- using (598)
|
||||
- using (600)
|
||||
- probably (586)
|
||||
- always (574)
|
||||
- course (569)
|
||||
- though (567)
|
||||
- though (568)
|
||||
- similar (565)
|
||||
- https (565)
|
||||
- similar (564)
|
||||
- basically (554)
|
||||
- really (538)
|
||||
- someone (536)
|
||||
- someone (537)
|
||||
- memory (535)
|
||||
- actually (534)
|
||||
- actually (535)
|
||||
|
||||
latest changes:
|
||||
|
||||
```
|
||||
Date: Sat Dec 14 16:25:29 2024 +0100
|
||||
debugging.md
|
||||
disease.md
|
||||
drummyfish.md
|
||||
free_software.md
|
||||
freedom.md
|
||||
git.md
|
||||
just_werks.md
|
||||
lgbt.md
|
||||
often_confused.md
|
||||
palette.md
|
||||
random_page.md
|
||||
shortcut_thinking.md
|
||||
soyence.md
|
||||
suicide.md
|
||||
trolling.md
|
||||
wiki_pages.md
|
||||
wiki_stats.md
|
||||
work.md
|
||||
xxiivv.md
|
||||
Date: Fri Dec 13 20:40:56 2024 +0100
|
||||
90s.md
|
||||
freedom.md
|
||||
|
|
@ -104,29 +124,6 @@ Date: Fri Dec 13 20:40:56 2024 +0100
|
|||
wiki_pages.md
|
||||
wiki_stats.md
|
||||
Date: Thu Dec 12 21:58:18 2024 +0100
|
||||
adam_smith.md
|
||||
binary.md
|
||||
bit_hack.md
|
||||
bloat.md
|
||||
feminism.md
|
||||
gay.md
|
||||
hitler.md
|
||||
homelessness.md
|
||||
human_language.md
|
||||
island.md
|
||||
logic_gate.md
|
||||
needed.md
|
||||
project.md
|
||||
random_page.md
|
||||
rust.md
|
||||
smallchesslib.md
|
||||
stereotype.md
|
||||
trolling.md
|
||||
unary.md
|
||||
wiki_pages.md
|
||||
wiki_stats.md
|
||||
work.md
|
||||
youtube.md
|
||||
```
|
||||
|
||||
most wanted pages:
|
||||
|
|
@ -160,27 +157,27 @@ most popular and lonely pages:
|
|||
- [bloat](bloat.md) (226)
|
||||
- [free_software](free_software.md) (194)
|
||||
- [game](game.md) (147)
|
||||
- [suckless](suckless.md) (145)
|
||||
- [suckless](suckless.md) (146)
|
||||
- [proprietary](proprietary.md) (132)
|
||||
- [minimalism](minimalism.md) (113)
|
||||
- [censorship](censorship.md) (112)
|
||||
- [modern](modern.md) (111)
|
||||
- [computer](computer.md) (107)
|
||||
- [computer](computer.md) (108)
|
||||
- [kiss](kiss.md) (106)
|
||||
- [fun](fun.md) (104)
|
||||
- [programming](programming.md) (101)
|
||||
- [math](math.md) (100)
|
||||
- [gnu](gnu.md) (96)
|
||||
- [gnu](gnu.md) (97)
|
||||
- [shit](shit.md) (95)
|
||||
- [linux](linux.md) (95)
|
||||
- [fight_culture](fight_culture.md) (93)
|
||||
- [bullshit](bullshit.md) (91)
|
||||
- [fight_culture](fight_culture.md) (94)
|
||||
- [bullshit](bullshit.md) (92)
|
||||
- [woman](woman.md) (90)
|
||||
- [hacking](hacking.md) (90)
|
||||
- [corporation](corporation.md) (87)
|
||||
- [less_retarded_society](less_retarded_society.md) (86)
|
||||
- [corporation](corporation.md) (86)
|
||||
- [free_culture](free_culture.md) (85)
|
||||
- [art](art.md) (84)
|
||||
- [art](art.md) (85)
|
||||
- [public_domain](public_domain.md) (83)
|
||||
- [pseudoleft](pseudoleft.md) (83)
|
||||
- [chess](chess.md) (83)
|
||||
|
|
|
|||
17
work.md
17
work.md
|
|
@ -33,19 +33,22 @@ For lawyer cunts: we officially DO NOT ADVISE any illegal methods mentioned here
|
|||
- **Leeching welfare/neetbux**: it's a common practice to e.g. register at the employment office and then just take unemployment support. There are many other potential sources of state money, like the widow pension, money for children etc.
|
||||
- **Becoming caretaker of a relative**: in some countries you can become a caretaker for someone, usually a relative, who's old and/or disabled and needs a daily assistant, which will count as a job, you'll be getting some state money etc. So ask your grandma maybe, then just let her watch TV all day and do whatever you want with the free time.
|
||||
- **Convincing someone rich to just give you $$$**: low chance of success, but it can't hurt to just sincerely ask some millionaires if they could maybe drop $100K or something, maybe when the guy will do it if he's drunk or high or just likes you.
|
||||
- **"Religious reasons"**: adopt of even invent a "religion" that says you cannot work, for example Judaism forbids any work on Saturday (Sabbath) -- you may be able to dig up a religion that has a lot of holy days on which you mustn't work. If your employer protests, absolutely rape him in court for racism and oppression, sue him for at least $1000000000, you're guaranteed to win this.
|
||||
- **"Religious reasons"**: adopt or even invent a "religion" that says you cannot work, for example Judaism forbids any work on Saturday (Sabbath) -- you may be able to dig up a religion that has a lot of holy days on which you mustn't work. If your employer protests, absolutely rape him in court for racism and oppression, sue him for at least $1000000000, you're guaranteed to win this.
|
||||
- **Calling anonymous inspections**: it can be fine to [troll](trolling.md) one's employers by calling for example hygienic workplace inspections, one may for example call that he saw they mix in shit into food, that there are rats running around, that employees masturbate in workplace and so on. When inspection comes, workers may be left waiting and just relaxing or even staying at home, and if the inspection does find some violations (very likely), it may at least temporarily close the workplace, again winning a few days off for the slaves.
|
||||
- **Stealing from the rich**: stealing stuff from supermarkets, offices etc. is nice (officially NOT ADVISED, but it's still very nice). It's also helping society. Do not steal from the poor.
|
||||
- **Getting a rich partner?**: someone rich can just take care of you for sex and love, however it may be not worth it as rich people are often capitalists whom it's better to stay away from.
|
||||
- **Moving to some nice community that doesn't force work**: the problem is actually finding such community, but maybe some hippie tent villages could be like that -- look up *mutual aid networks*. Multiple people living together can be an advantage, they may pool in money to pay the absolutely necessary bills like property tax -- this will spread the expenses over many people so that every member will have to pay just a very small amount per year. They may then use their land to establish a micro community that works on [communist](communism.md) principles, making their own food etc.
|
||||
- **Going to [jail](jail.md)**: in some countries jail are quite luxurious and once in jail you can just refuse to work as they cannot lock you up more. In jail you have shelter and food, i.e. already more than most people in a capitalist society. However watch out: for some crimes you may just get fined, not actually locked up, so it's good to study the law to know which crimes it's best to commit to safely get one to jail. Your inspiration may be David Hampson who repeatedly gets himself arrested by standing in the middle of the road and then just refuses to talk to anyone.
|
||||
- **US edition: suing the employer**: If you're a woman, nowadays you can successfully sue anyone for rape, you don't even need evidence, making $1000000 shouldn't be a problem. A non-white can play it on [racism](racism.md), a "disabiled" man can play it on disability etc. However one mustn't hurt a fellow working class poorfag, it must be made so that the comapany or some rich manager pays. IN THEORY it is possible to plot with one's coworkers -- for example the coworkers on same positions talk to each other, reveal their pays to one another, then the one with lowest pay sues for discrimination and they split the profit. Etc.
|
||||
- **Becoming a prostitute (usually for [women](woman.md))**: it's easy money and you literally get paid for having [sex](sex.md). Unless you're real ugly it may be enough to just "work" like this for a few days in a month.
|
||||
- **The gypsy way: making tons of children**: gypsies managed to [hack](hacking.md) the system by just making 10, 15 or maybe 20 children -- not only you stay on maternal leave, but you can take financial support for every one of them.
|
||||
- **Going to [jail](jail.md)**: in some countries prisons are quite luxurious and once in jail you can just refuse to work as they cannot lock you up more. In jail you have shelter and food, i.e. already more than most people in a capitalist society. However watch out: for some crimes you may just get fined, not actually locked up, so it's good to study the law to know which crimes it's best to commit to safely get one to jail. Your inspiration may be David Hampson who repeatedly gets himself arrested by standing in the middle of the road and then just refuses to talk to anyone.
|
||||
- **Moving to area where disasters happen regularly**, like some highly earthquake rich land, may allow one to just jump charities. It's hard to keep businesses running under a volcano that erupts every other week, so you just run around from charity tent to another one, get food, free healthcare etc. It may also be a nice, adventurous life.
|
||||
- **US edition: suing the employer**: If you're a [woman](woman.md), nowadays you can successfully sue anyone for rape, you don't even need evidence, making $1000000 shouldn't be a problem. A non-white can play it on [racism](racism.md), a "disabiled" man can play it on disability etc. However one mustn't hurt a fellow working class poorfag, it must be made so that the comapany or some rich manager pays. IN THEORY it is possible to plot with one's coworkers -- for example the coworkers on same positions talk to each other, reveal their pays to one another, then the one with lowest pay sues for discrimination and they split the profit. Etc.
|
||||
- **Becoming a prostitute (usually for [women](woman.md))**: it's easy money and you literally get paid for having [sex](sex.md). Unless you're real ugly it may be enough to just "work" like this for a few days in a month. With shit like OnlyFans you don't even have to actually have real sex or risk STDs, it's literally like godmode cheat for women.
|
||||
- **The gypsy way: making tons of children**: gypsies managed to [hack](hacking.md) the system by just making 10, 15 or maybe 20 children -- not only you stay on maternal leave, but you can take financial support for every one of them. The genius of this method is that since CHILDREN ARE MAGICAL, the state HAS TO make sure children are properly cared for AND at the same time it's difficult (e.g. enraging to [feminists](feminism.md) but even just general public) and messy to separate children from their mother, SO as long as a woman is a mother of a non-adult child, she can just 100% refuse to work and the state has no other choice than throw money at her so that the children (and the mother along with them) are fine. So a woman just makes 2 or 3 children, then as they're reaching 18 she makes another and so on until old age. The only danger is in actually getting the children taken away, so a big stress is on NOT taking drugs, NOT drinking, NOT doing idiotic shit like beating the children, NOT whoring for more money and so on.
|
||||
- **Widow pension**: sometimes there is a widow pension, so you can quickly marry someone who is dying, then you'll be forever getting free money.
|
||||
- **The feminist way: if you're a [woman](woman.md), you can sue a random millionaire for [rape](rape.md)**. This works every time, you can just make everything up, the guy will be forced to pay you a billion or two, no evidence needed, just cry in the court.
|
||||
- **Alcoholism**: starting to drink heavily may remove your brain brain, but then suddenly you'll also be judged a "victim" of alcoholism, locked somewhere and probably won't have to work, so it may be worth it.
|
||||
- **Getting EU (or similar) money on some bullshit** -- if this was to be considered """fraud""", then we officially DO NOT RECOMMEND THIS (:D), but it is very nice if someone does it. This would require the hypothetical man to maybe do some small amount of "work", but he could just dig a lot of money for doing almost nothing, for example one may ask for money for some software project that looks like a 100K EUR 1 year project -- this would actually be true if you made the project the "normal" way (i.e. using bloat tech, hiring consultants, managers, lawyers and whatever), but you can just do the project in a simple, [LRS](lrs.md) way over the weekend alone, then enjoy a whole year off as well as your free money.
|
||||
- **Alcoholism**: starting to drink heavily may remove your brain, but then suddenly you'll also be judged a "victim" of alcoholism, locked somewhere and probably won't have to work, so it may be worth it. You don't need brain to lead average life in [21st century](21st_century.md).
|
||||
- **Getting EU (or similar) money on some [bullshit](bullshit.md)** -- if this was to be considered """fraud""", then we officially DO NOT RECOMMEND THIS (:D), but it is very nice if someone does it. This would require the hypothetical man to maybe do some small amount of "work", but he could just dig a lot of money for doing almost nothing, for example one may ask for money for some software project that looks like a 100K EUR 1 year project -- this would actually be true if you made the project the "normal" way (i.e. using bloat tech, hiring consultants, managers, lawyers and whatever), but you can just do the project in a simple, [LRS](lrs.md) way over the weekend alone, then enjoy a whole year off as well as your free money.
|
||||
- **Comfy [homeless](homelessness.md) life.** May be super cool if you for example just inherited family fortune, then you sell everything and just live super frugally, you won't even have to beg too much.
|
||||
- **Moving to jungle and becoming God of some primitive tribe.** Just bring some magic electronic devices with you, show them soul stealing photos, take a gun and show them you are capable of magically killing at distance, show you can conjure fire from your hands with a lighter. Then just sit on the throne and let yourself be fed.
|
||||
- **[Sucicide](suicide.md)**: obviously death solves all problems. TBH lying in ground is probably more comfy than being raped every day of the year for 120 years.
|
||||
- For discovering other methods it might be useful to dig in similar topics such as avoiding military service. For example breathing cacao before the medical entry examination was a popular way to simulate lung disease in the past -- nowadays with better technology this may no longer work, but still at least useful hints and directions may be found this way.
|
||||
- ...
|
||||
|
|
|
|||
Loading…
Reference in a new issue